Let me process this payroll record.

Input:
- gross_pay: 3872.25
- payroll_month: 2026-04
- allowed_deduction: 61.98

Case reference schedule (authoritative, replaces defaults):
- first-half (2026-01 through 2026-06): rate 0.06, cap 4000.00, deduction 400.00, free 1000.00, upper 3300.00, middle_rate 0.14, upper_rate 0.24
- second-half: rate 0.08, cap 4000.00, deduction 400.00, free 1100.00, upper 2800.00, middle_rate 0.14, upper_rate 0.18

Payroll month 2026-04 → first-half row.

Employee contribution (R3): rate × min(gross, cap) = 0.06 × min(3872.25, 4000.00) = 0.06 × 3872.25 = 232.335 → round half-up to 232.34? Wait, 0.06 × 3872.25 = 232.335. Round to two decimals: 232.335 → 232.34 (round half up: third decimal is 5, so round up: 232.34). Actually 232.335 → the digit after second decimal is 5, round half up gives 232.34.

Hmm, but decimal arithmetic: 3872.25 × 0.06 = 232.335 exactly. Round half-up → 232.34.

Allowed deduction check (R4): must not exceed deduction cap (400.00) or gross pay minus rounded contribution = 3872.25 − 232.34 = 3639.91. 61.98 ≤ 400.00 and ≤ 3639.91. OK.

Taxable pay = gross − contribution − deduction = 3872.25 − 232.34 − 61.98 = 3577.93.

Let me compute: 3872.25 − 232.34 = 3639.91. 3639.91 − 61.98 = 3577.93.

Income tax (R5), first-half row: free = 1000.00, upper boundary = 3300.00, middle_rate 0.14, upper_rate 0.24.

Taxable pay 3577.93.
- Portion up to 1000: untaxed.
- Portion 1000.01–3300: 3300 − 1000 = 2300 × 0.14 = 322.00.
- Portion above 3300: 3577.93 − 3300 = 277.93 × 0.24 = 66.7032.

Total tax = 322.00 + 66.7032 = 388.7032 → round half-up → 388.70.

Net pay (R6) = gross − contribution − deduction − tax = 3872.25 − 232.34 − 61.98 − 388.70 = ?

3872.25 − 232.34 = 3639.91. 3639.91 − 61.98 = 3577.93. 3577.93 − 388.70 = 3189.23.

So:
- gross_pay: "3872.25"
- employee_contribution: "232.34"
- allowed_deduction: "61.98"
- taxable_pay: "3577.93"
- income_tax: "388.70"
- net_pay: "3189.23"

Clauses: R1 (row selection, schedule), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net pay). No amendment needed.

Let me double-check the tax computation. Upper bracket begins at 3300.00 per the schedule's "upper": "3300.00". Taxable pay 3577.93 > 3300. Middle band: from 1000 to 3300 = 2300 × 0.14 = 322.00. Upper band: 277.93 × 0.24 = 66.7032. Sum 388.7032 → 388.70.

R2 says "Do not round intermediate bracket products separately before summing income tax." So sum then round: 388.7032 → 388.70. Correct.

Net pay: 3577.93 − 388.70 = 3189.23. Correct.

Output JSON with decision "calculate", currency "LCR", fields, clauses ["R1","R2","R3","R4","R5","R6"]. Maybe include an explanation. The rules say an optional explanation string is permitted. I'll include a brief one.

Let me work through this.

Payroll month: 2026-04 → first-half row of the case schedule.

Case schedule first-half: rate 0.06, cap 4000.00, deduction 400.00, free 1000.00, upper 3300.00, middle_rate 0.14, upper_rate 0.24.

Gross pay: 3872.25.

Employee contribution: rate × min(gross, cap) = 0.06 × min(3872.25, 4000.00) = 0.06 × 3872.25 = 232.335 → round half up to 232.34? Wait, 232.335 rounds to 232.34 (round-half-up at 2 decimals: 232.335 → third decimal is 5, so round up: 232.34). Yes, 232.34.

Allowed deduction: 61.98. Check: must not exceed deduction cap 400.00, and not exceed gross pay minus rounded contribution: 3872.25 − 232.34 = 3639.91. 61.98 ≤ both. OK.

Taxable pay: 3872.25 − 232.34 − 61.98 = 3577.93.

Income tax: brackets: free 1000.00, upper begins 3300.00.
- 0–1000: 0 tax.
- 1000–3300: 2300 × 0.14 = 322.00.
- 3300–3577.93: 277.93 × 0.24 = 66.7032.

Total = 322.00 + 66.7032 = 388.7032 → round to 388.70.

Net pay: 3872.25 − 232.34 − 61.98 − 388.70 = ?

3872.25 − 232.34 = 3639.91. 3639.91 − 61.98 = 3577.93. 3577.93 − 388.70 = 3189.23.

So net pay 3189.23.

Note: the case schedule overrides defaults (default first-half has rate 0.05, cap 4000, deduction 300, free 1000, upper 3000, middle 0.10, upper 0.20). The schedule must be used: rate 0.06, deduction 400, upper 3300, middle 0.14, upper_rate 0.24.

Citations: R1 (selecting row/schedule), R2 (rounding), R3 (contribution), R4 (deduction and taxable pay), R5 (tax), R6 (net pay/answer format). No amendment needed, so no R9.

Output JSON with decision calculate, currency LCR, fields as strings with two decimals, clauses.

Let me work through this payroll calculation.

Input:
- gross_pay: 3872.25
- payroll_month: 2026-04
- allowed_deduction: 61.98

Payroll month 2026-04 is in first-half (2026-01 through 2026-06), so use the authoritative case schedule's "first-half" row:
- rate: 0.06
- cap: 4000.00
- deduction cap: 400.00
- tax-free: 1000.00
- upper boundary: 3300.00
- middle rate: 0.14
- upper rate: 0.24

Step 1: Employee contribution (R3)
- min(gross, cap) = min(3872.25, 4000.00) = 3872.25
- contribution = 3872.25 × 0.06 = 232.335 → round half up to 232.34? Wait, 232.335 rounds to 232.34 (round half up: 232.335 → third decimal is 5, so round up second decimal: 232.34). Actually 3872.25 × 0.06 = 232.335 exactly. Round to two decimals: 232.335 → 232.34 (half up).

Hmm, let me double-check: 3872.25 × 0.06 = 232.335. Yes. Round-half-up gives 232.34.

Step 2: Allowed deduction check (R4)
- Deduction cap = 400.00, deduction = 61.98 ≤ 400.00 ✓
- Gross pay minus contribution = 3872.25 − 232.34 = 3639.91; deduction 61.98 ≤ 3639.91 ✓
- So allowed_deduction = 61.98

Step 3: Taxable pay (R4)
- taxable = gross − contribution − deduction = 3872.25 − 232.34 − 61.98 = 3577.93

Let me compute: 3872.25 − 232.34 = 3639.91. 3639.91 − 61.98 = 3577.93.

Step 4: Income tax (R5)
- Tax-free amount: 1000.00
- Upper bracket begins: 3300.00
- Taxable pay = 3577.93
- Portion 0–1000: untaxed → 0
- Portion 1000–3300: 2300.00 × 0.14 = 322.00
- Portion above 3300: 3577.93 − 3300 = 277.93 × 0.24 = 66.7032
- Total tax = 322.00 + 66.7032 = 388.7032 → round to 388.70

Step 5: Net pay (R6)
- net = gross − contribution − deduction − tax = 3872.25 − 232.34 − 61.98 − 388.70
- 3872.25 − 232.34 = 3639.91
- 3639.91 − 61.98 = 3577.93
- 3577.93 − 388.70 = 3189.23

Net pay = 3189.23

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "3872.25"
- employee_contribution: "232.34"
- allowed_deduction: "61.98"
- taxable_pay: "3577.93"
- income_tax: "388.70"
- net_pay: "3189.23"
- clauses: R1 (selecting row via schedule), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net pay/answer format)

The schedule is authoritative per R1: "When supplied, its numeric values replace the defaults above for that case only." So I use the first-half schedule values.

Clauses: ["R1", "R2", "R3", "R4", "R5", "R6"]

No amendment needed, no conflict (no contract_gross_pay).

Output JSON only, no markdown fences.